Answer :
Answer:
[tex]a_{n} = 12 + (n - 1) (-5)[/tex]
Step-by-step explanation:
An explicit formula has two parts in it.
1) The initial value i.e. [tex]a_{1} = 12[/tex]
2) The common difference between consecutive terms
To find the common difference we will use the first 5 terms which are as follow
12, 7, 2, -3, -8
the common difference is of -5
The general formula for an explicit arithmetic equation is as follow
[tex]a_{n} = a_{1} + (n-1) d\\[/tex]
(This is an arithmetic sequence since it has a common difference)
Where
[tex]a_{1}[/tex] is the initial value
[tex]n[/tex] is the nth term
[tex]d[/tex] is the common difference
hence the explicit formula becomes
[tex]a_{n} = 12 + (n - 1) (-5)[/tex]